TRANSIENT RESPONSE OF VISCOELASTIC MOVING BELTS USING BLOCK-BY-BLOCK METHOD

2002 ◽  
Vol 02 (02) ◽  
pp. 265-280 ◽  
Author(s):  
LIXIN ZHANG ◽  
JEAN W. ZU ◽  
Z. ZHONG
Keyword(s):  
Integral Equations ◽  
Transient Response ◽  
Governing Equation ◽  
Axial Velocity ◽  
Constitutive Law ◽  
System Response ◽  
Block Method ◽  
Viscoelastic Characteristic ◽  
Viscoelastic Parameters ◽  
Linear Viscoelastic

The linear, viscoelastic, integral constitutive law is employed to model the viscoelastic characteristic of belt materials. By assuming the translating eigenfunctions instead of stationary eigenfunctions to be the spatial solutions, the governing equation is reduced to differential-integral equations in time, which are then solved by the block-by-block method. The transient amplitudes of parametrically excited viscoelastic moving belts with uniform and non-uniform travelling speed are obtained. The effects of viscoelastic parameters and perturbed axial velocity on the system response are also investigated.

Nonlinear Vibration of Parametrically Excited Viscoelastic Moving Belts

1999 ◽  
Author(s):  
Lixin Zhang ◽  
Jean W. Zu
Keyword(s):  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Equation Of Motion ◽  
Generalized Equation ◽  
Constitutive Law ◽  
Parametrically Excited ◽  
Viscoelastic Parameters ◽  
Linear Viscoelastic ◽  
Existence Conditions ◽  
Gyroscopic Systems

Abstract The dynamic response and stability of parametrically excited viscoelastic belts are investigated in this paper. The linear viscoelastic differential constitutive law is employed to characterize the material property of belts. The generalized equation of motion is obtained for a viscoelastic moving belt with geometric nonlinearity. The method of multiple scales is applied directly to the governing equation, which is in the form of continuous gyroscopic systems. Closed-form expressions for the amplitude, existence conditions and stability conditions of non-trivial limit cycles of the summation resonance are obtained. Effects of viscoelastic parameters, excitation frequencies, excitation amplitudes and axial moving speeds on stability boundaries are discussed.

Prediction of the Transient Response of a Linear Viscoelastic Solid

1966 ◽  
Vol 33 (2) ◽  
pp. 449-450 ◽  
Author(s):  
W. G. Gottenberg ◽  
R. M. Christensen
Keyword(s):  
Transient Response ◽  
Viscoelastic Solid ◽  
Linear Viscoelastic

Principal parametric resonance of axially accelerating viscoelastic strings with an integral constitutive law

2005 ◽  
Vol 461 (2061) ◽  
pp. 2701-2720 ◽  
Author(s):  
Li-Qun Chen
Keyword(s):  
Steady State ◽  
Parametric Resonance ◽  
Multiple Scales ◽  
Constitutive Law ◽  
Transverse Motion ◽  
Viscoelastic Parameters ◽  
Principal Parametric Resonance ◽  
Linearized Stability ◽  
Speed Fluctuation ◽  
Axial Speed

The steady-state transverse responses and the stability of an axially accelerating viscoelastic string are investigated. The governing equation is derived from the Eulerian equation of motion of a continuum, which leads to the Mote model for transverse motion. The Kirchhoff model is derived from the Mote model by replacing the tension with the averaged tension over the string. The method of multiple scales is applied to the two models in the case of principal parametric resonance. Closed-form expressions of the amplitudes and the existence conditions of steady-state periodical responses are presented. The Lyapunov linearized stability theory is employed to demonstrate that the first (second) non-trivial steady-state response is always stable (unstable). Numerical calculations show that the two models are qualitatively the same, but quantitatively different. Numerical results are also presented to highlight the effects of the mean axial speed, the axial-speed fluctuation amplitude, and the viscoelastic parameters.

On the theory of sea‐floor conductivity mapping using transient electromagnetic systems

Geophysics ◽  
1987 ◽  
Vol 52 (2) ◽  
pp. 204-217 ◽  
Author(s):  
S. J. Cheesman ◽  
R. N. Edwards ◽  
A. D. Chave
Keyword(s):  
Half Space ◽  
Magnetic Dipole ◽  
Transient Response ◽  
System Response ◽  
Sea Floor ◽  
Closed Form Solutions ◽  
Dipole System ◽  
Transient Electromagnetic ◽  
A Minor ◽  
Resistive Zone

The electrical conductivity of the sea floor is usually much less than that of the seawater above it. A theoretical study of the transient step‐on responses of some common controlled‐source, electromagnetic systems to adjoining conductive half‐spaces shows that two systems, the horizontal, in‐line, electric dipole‐dipole and horizontal, coaxial, magnetic dipole‐dipole, are capable of accurately measuring the relatively low conductivity of the sea floor in the presence of seawater. For these systems, the position in time of the initial transient is indicative of the conductivity of the sea floor, while at distinctly later times, a second characteristic of the transient is a measure of the seawater conductivity. The diagnostic separation in time between the two parts of the transient response does not occur for many other systems, including several systems commonly used for exploration on land. A change in the conductivity of the sea floor produces a minor perturbation in what is essentially a seawater response. Some transient responses which could be observed with a practical, deep‐towed coaxial magnetic dipole‐dipole system located near the sea floor are those for half‐space, the layer over a conductive or resistive basement, and the half‐space with an intermediate resistive zone. The system response to two adjoining half‐spaces, representing seawater and sea floor, respectively, is derived analytically. The solution is valid for all time, provided the conductivity ratio is greater than about ten, or less than about one‐tenth. The analytic theory confirms the validity of numerical evaluations of closed‐form solutions to these layered‐earth models. A lateral conductor such as a vertical, infinite, conductive dike outcropping at the sea floor delays the arrival of the initial crustal transient response. The delay varies linearly with the conductance of the dike. This suggests that time delay could be inverted directly to give a measure of the anomalous integrated conductance of the sea floor both between and in the vicinity of the transmitter and the receiver dipoles.

Analytical Determination of Shock Response Spectra for an Impulse-Loaded Proportionally Damped System

Volume 1 ◽  
2004 ◽  
Author(s):  
R. David Hampton ◽  
Nathan S. Wiedenman ◽  
Ting H. Li
Keyword(s):  
Transient Response ◽  
Shock Loading ◽  
Response Spectrum ◽  
Response Spectra ◽  
Analytical Determination ◽  
System Response ◽  
Mechanical Shock ◽  
Shock Response ◽  
Mass Spring ◽  
The Impact

Many military systems must be capable of sustained operation in the face of mechanical shocks due to projectile or other impacts. The most widely used method of quantifying a system’s vibratory transient response to shock loading is called the shock response spectrum (SRS). The system response for which the SRS is to be determined can be due, physically, either to a collocated or to a noncollocated shock loading. Taking into account both possibilities, one can define the SRS as follows: the SRS presents graphically the maximum transient response (output) of an imaginary ideal mass-spring-damper system at one point on a flexible structure, to a particular mechanical shock (input) applied to an arbitrary (perhaps noncollocated) point on the structure, as a function of the natural frequency of the imaginary mass-spring-damper system. For a response point sufficiently distant from the impact area, many Army platforms (such as vehicles) can be accurately treated as linear systems with proportional damping. In such cases the output due to an impulsive mechanical-shock input can be decomposed into exponentially decaying sinusoidal components, using normal-mode orthogonalization. Given a shock-induced loading comprising such components, this paper provides analytical expressions for the various common SRS forms. The analytical approach to SRS-determination can serve as a verification of, or an alternative to, the numerical approaches in current use for such systems. No numerical convolution is required, because the convolution integrals have already been accomplished analytically (and exactly), with the results incorporated into the algebraic expressions for the respective SRS forms.

Modeling the System and Component Performance Interactions of a SOFC Based APU for Changes in Application Load: Transient Response and Control Strategy

2004 ◽  
Author(s):  
D. F. Rancruel ◽  
M. R. von Spakovsky
Keyword(s):  
Transient Response ◽  
Control Strategy ◽  
Control Strategies ◽  
Control Variable ◽  
System Level ◽  
System Component ◽  
System Response ◽  
Optimal Control Strategy ◽  
Synthesis Design ◽  
And Control

Solid-Oxide-Fuel-Cell (SOFC) stacks respond in seconds to changes in load while the balance of plant subsystem (BOPS) responds in times several orders of magnitude higher. This dichotomy diminishes the reliability and performance of SOFC electrodes with changes in load. In the same manner current and voltage ripples which result from particular power electronic subsystem (PES) topologies and operation produce a negative effect on the SOFC stack subsystem (SS) performance. The difference in transient response among the sub-systems must be approached in a way which makes operation of the entire system not only feasible but ensures that efficiency and power density, fuel utilization, fuel conversion, and system response are optimal at all load conditions. Thus, a need exists for the development of transient component- and system-level models of SOFC based auxiliary power units (APUs), i.e. coupled BOPS, SS, and PES, and the development of methodologies for optimizing subsystem responses and for investigating system-interaction issues. In fact the transient process occurring in a SOFC based APU should be systematically treated during the entire creative process of synthesis, design, and operational control, leading in its most general sense to a dynamic optimization problem. This entails finding an optimal system/component synthesis/design, taking into account on- and off-design operation, which in turn entails finding an optimal control strategy and control profile for each sub-system/component and control variable. Such an optimization minimizes an appropriate objective function while satisfying all system constraints. A preliminary set of chemical, thermal, electrochemical, electrical, and mechanical models based on first principles and validated with experimental data have been developed and implemented using a number of different platforms. These models have been integrated in order to be able to perform component, subsystem, and system analyses as well as develop optimal syntheses/designs and control strategies for transportation and stationary SOFC based APUs. Some pertinent results of these efforts are presented here.

Extraction of Quasi-Linear Viscoelastic Parameters for Lower Limb Soft Tissues From Manual Indentation Experiment

1999 ◽  
Vol 121 (3) ◽  
pp. 330-339 ◽  
Author(s):  
Y. P. Zheng ◽  
A. F. T. Mak
Keyword(s):  
Lower Limb ◽  
Soft Tissues ◽  
Model Parameters ◽  
Viscoelastic Parameters ◽  
Fitting Procedure ◽  
Ultrasound Indentation ◽  
Initial Modulus ◽  
Linear Viscoelastic ◽  
Young Subjects ◽  
Three Body

A manual indentation protocol was established to assess the quasi-linear viscoelastic (QLV) properties of lower limb soft tissues. The QLV parameters were extracted using a curve-fitting procedure on the experimental indentation data. The load-indentation responses were obtained using an ultrasound indentation apparatus with a hand-held pen-sized probe. Limb soft tissues at four sites of eight normal young subjects were tested in three body postures. Four QLV model parameters were extracted from the experimental data. The initial modulus E0 ranged from 0.22 kPa to 58.4 kPa. The nonlinear factor E1 ranged from 21.7 kPa to 547 kPa. The time constant τ ranged from 0.05 s to 8.93 s. The time-dependent material parameter α ranged from 0.029 to 0.277. Large variations of the parameters were noted among subjects, sites, and postures.

Response of a Squeeze Film Damper-Elastic Structure System to Multiple and Consecutive Impact Loads

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Luis San Andrés ◽  
Sung-Hwa Jeung
Keyword(s):  
Transient Response ◽  
Damping Ratio ◽  
Test System ◽  
Elastic Structure ◽  
Squeeze Film ◽  
Radial Clearance ◽  
System Response ◽  
Fluid Inertia ◽  
Squeeze Film Dampers ◽  
Structural Isolation

Squeeze film dampers (SFDs) are common in aircraft gas turbine engines, customized to provide a desired level of damping while also ensuring structural isolation. This paper presents measurements obtained in a test rig composed of a massive cartridge, an elastic structure, and an open-ends SFD with length L = 25.4 mm, diameter D = 127 mm, and radial clearance c = 0.267 mm. ISO VG 2 oil at room temperature lubricates the thin film. The measurements quantify the system transient response to sudden loads for motions departing from various static eccentricity displacements, es/c = 0–0.6. The batch of tests include recording the system response to (a) one single impact, (b) two (and three) impacts with an elapsed time of 30 ms in between, and (c) two or more consecutive impacts, without any delay, each with a load magnitude at 50% of the preceding impact. The load actions intend to reproduce, for example, a hard landing on an uneven surface or plunging motions from sudden contacts in a machine tool. The test system transient responses due to one or more impacts, each 30 ms apart, show the peak amplitude of motion (ZMAX) is proportional to the magnitude of applied load (FMAX). The identified system damping ratio (ξ) is proportional to the peak dynamic displacement as a linear system would show. Predictions of transient response from a physical SFD model accounting for fluid inertia correlate best with the experimental results as they produce greatly reduced peak dynamic motions when compared to predictions from a purely viscous SFD model. For the responses due to consecutive impacts, one after the other with no delay, the system motion does not decay immediately but builds to produce larger motion amplitudes than in the earlier cases. Eventually, as expected, after several oscillations, the system comes to rest. For an identical damper having a smaller clearance cs = 0.213 mm (0.8c), its damping ratio (ξs) is ∼1.3 to ∼1.7 times greater than the damping ratio for the damper with a larger film clearance (ξ). Hence, the experimentally derived (ξs/ξ) scales with (c/cs)2. The finding demonstrates the importance of manufacturing precisely the components in a damper to produce an accurate clearance.

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